Aug, 2019
Domain-complete and LCS-complete Spaces
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
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- Volume
- 345
- Number
- First page
- 3
- Last page
- 35
- Language
- English
- Publishing type
- Research paper (international conference proceedings)
- DOI
- 10.1016/j.entcs.2019.07.014
- Publisher
- ELSEVIER
We study G(delta) subspaces of continuous dcpos, which we call domain-complete spaces, and G(delta) subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in particular, all continuous dcpos-, all topologically complete spaces in the sense of Cech, and all quasi-Polish spaces-in particular, all Polish spaces. We show that LCS-complete spaces are sober, Wilker, compactly Choquet-complete, completely Baire, and circle dot-consonant-in particular, consonant; that the countably-based LCS-complete (resp., domain-complete) spaces are the quasi-Polish spaces exactly; and that the metrizable LCS-complete (resp., domain-complete) spaces are the completely metrizable spaces. We include two applications: on LCS-complete spaces, all continuous valuations extend to measures, and sublinear previsions form a space homeomorphic to the convex Hoare powerdomain of the space of continuous valuations.
- Link information
- ID information
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- DOI : 10.1016/j.entcs.2019.07.014
- ISSN : 1571-0661
- Web of Science ID : WOS:000483310000002